Effect of water flow and chemical environment onmicrobiota growth and composition in thehuman colonJonas Cremera,1,2, Markus Arnoldinia,1,2, and Terence Hwaa,2

aDepartment of Physics, University of California, San Diego, La Jolla, CA 92093-0374

Edited by David R. Nelson, Harvard University, Cambridge, MA, and approved May 9, 2017 (received for review November 29, 2016)

The human gut harbors a dynamic microbial community whosecomposition bears great importance for the health of the host. Here,we investigate how colonic physiology impacts bacterial growth,which ultimately dictates microbiota composition. Combining mea-surements of bacterial physiology with analysis of published dataon human physiology into a quantitative, comprehensive modelingframework, we show how water flow in the colon, in concert withother physiological factors, determine the abundances of the majorbacterial phyla. Mechanistically, our model shows that local pH valuesin the lumen, which differentially affect the growth of different bac-teria, drive changes in microbiota composition. It identifies key factorsinfluencing the delicate regulation of colonic pH, including epithelialwater absorption, nutrient inflow, and luminal buffering capacity, andgenerates testable predictions on their effects. Our findings show thata predictive andmechanistic understanding of microbial ecology in thegut is possible. Such predictive understanding is needed for the ratio-nal design of intervention strategies to actively control the microbiota.

gut microbiota | colon physiology | water absorption | stool consistency |colonic pH

The human gut microbiota is composed of trillions of bacterialcells (1–4) from several hundred species (1–3, 5, 6). Over the

last two decades, a multitude of studies have shown a strong impactof human health status on the composition of this microbiota, and inturn a strong effect of microbiota composition on host physiology hasalso been confirmed (7–9). Various intervention strategies are beinginvestigated to modify the microbiota composition via prebiotics andprobiotics (10). Despite this importance for human health, little isknown about how the microbiota composition is shaped by the in-terplay between human and bacterial physiology in the gut.In this study, we present a physiological model that quantitatively

describes this host–microbiota interplay. Our model is based on ahydrodynamic perspective, which posits that bacterial densitiesreached in the colon result from a dynamic balance between bac-terial growth, flow through the colon, and peristaltic mixing (11). Tobuild the present model, we extensively analyzed literature data onhuman gut physiology to obtain quantitative estimates for a range ofrelevant host parameters. We further characterized the rates ofbacterial growth, carbohydrate consumption, and fermentationproduct excretion for representatives of the two dominant bacteriaphyla, Bacteroidetes and Firmicutes, that typically make up morethan 90% of the bacterial cells observed in the gut (6).Combining these aspects of human and bacterial physiology into

a coarse-grained mathematical model allowed us to study bacterialgrowth dynamics in the human gut. Without resorting to ad hocfitting parameters, model results are in quantitative agreement withavailable data on key observables of human gut physiology. We findthat changes in pH values in the colon that are due to the secretionof acidic fermentation products and shaped by human physiology(such as flow through the colon, mixing of colonic contents, epi-thelial absorption of water and fermentation products) are key tounderstanding changes in microbiota composition: by their fer-mentative mode of growth, members of the gut microbiota areforced to acidify their environment, and because different speciesexhibit different sensitivities to pH changes, this internal feedback

changes the microbiota composition. In addition, the model al-lows us to investigate the dependence of microbiota compositionon important physiological characteristics of the host, such asnutrient influx and water absorption, which are amenable totherapeutic intervention.

ResultsA Model for Bacterial Growth in the Colon. The colonic environmentis mostly anaerobic, and the most abundant strains in the humanmicrobiota are obligate anaerobes. Due to the lack of oxygen asterminal electron acceptor, energy generation in the colon is largelyfermentative, and the excreted end products of this fermentationare mainly short-chain fatty acids (SCFAs). The high densities ofbacteria engaged in fermentation in the colon lead to high con-centrations of these acids. This, in turn, leads to a local drop in pH,affecting bacterial growth (12, 13).To quantitatively understand this pH change and its influence on

bacterial growth physiology in the gut, we first conducted controlledexperiments with Bacteroides thetaiotaomicron (Bt) and Eubacteriumrectale (Er), as members of the phyla Bacteroidetes and Firmicutes,respectively. These strains are among the 10 most abundant speciescommonly found in the human fecal microbiota (1) and have beenused as model strains representing their respective phyla (14). Wequantified SCFA secretion and biomass yields at different pH val-ues in anaerobic conditions. To estimate rates of fermentationproduct excretion and carbon utilization and the contribution ofspecific SCFAs to the total secreted products, we took samplesat different points during exponential growth, and measuredcarbohydrate consumption and the production of various

Significance

The human gut is populated by a dense microbial population,strongly impacting health and disease. Metagenomic sequencinghas led to crucial insights into microbiota changes in response tovarious perturbations, but a mechanistic understanding of thesechanges is largely missing. As the composition of the gut micro-biota is a consequence of bacterial growth, we propose an ap-proach that focuses on bacterial growth in the human largeintestine and the physiological factors influencing it. Using acombination of experimental analysis and quantitative simula-tions, we explain the observed variation in microbiota composi-tion among healthy humans and the dominant role of nutrientinflow and stool consistency. Our quantitative modeling frame-work is a step toward a predictive understanding of microbiotadynamics in the human host.

Author contributions: J.C., M.A., and T.H. designed research; J.C. and M.A. performedresearch; J.C., M.A., and T.H. analyzed data; and J.C., M.A., and T.H. wrote the paper.

The authors declare no conflict of interest.

This article is a PNAS Direct Submission.1J.C. and M.A. contributed equally to this work.2To whom correspondence may be addressed. Email: hwa@ucsd.edu, cremer@physics.ucsd.edu, or markus.arnoldini@gmail.com.

This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1619598114/-/DCSupplemental.

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fermentation products using HPLC (Materials and Methods).These data allowed us to estimate growth yields and total SCFAproduction for Bt and Er (Fig. 1 A and B and SI Appendix, Fig. S1).We also quantified growth rates at different pH values. Con-

firming previous results (15), Bt and Er are found to respond dif-ferently to changes in environmental pH values. Although Bt cangrow faster than Er at neutral pH, Er has a less sensitive growthresponse to a drop in pH than Bt, and is thus less affected by theacidification caused by fermentative growth (Fig. 1C). Dependingon SCFA abundance and how host physiology influences the localpH values (discussed below), this differential pH feedback can becrucial in determining microbiota composition (Fig. 1D). It hasbeen shown that the pH dependence of these two strains is quali-tatively representative of many abundant species in their respectivephyla; Duncan et al. (15) have tested 8 strains of the phylum Bac-teroidetes, and 20 strains of the phylum Firmicutes at three dif-ferent pH values, and consistently reported a less severe effect oflow pH on Firmicutes. To model a coarse-grained gut microbiotacomposed of the two dominant phyla, the Bacteroidetes and theFirmicutes (6), we used the experimental parameters derived for Btand Er (Fig. 1 and SI Appendix, Fig. S1).To understand the growth conditions these bacteria encounter in

the human colon, it is also essential to quantify the important as-pects of human physiology affecting bacterial growth dynamics.Water flow and mixing play important roles: Fluid entering theproximal colon (i.e., the cecum and ascending colon; Fig. 2A) car-ries very low bacterial load [∼107 cells per mL (16, 17)] and comesat a rate of 1.5–2 L/d (18). At such high flow rates (corresponding toflow velocities of J 30 μm=s; Fig. 2B), bacterial density in thelumen would quickly be depleted unless additional mechanisms arein place to keep them at the stable and high levels observed [1011 to1012 cells per mL (19)] (5, 11, 20, 21). We argue that hydrodynamic

mixing by active contractions of the intestinal walls—continuouslyobserved in the proximal colon (22)—is the most importantmechanism stabilizing high bacterial densities (Fig. 2C): In a recentin vitro study (11), it has been shown that hydrodynamic mixing, incombination with bacterial growth, allows maintenance of stablebacterial populations even for high flow rates; here, we discuss thesituation in the human gut in SI Appendix, Fig. S2 and section 2.3.Transport across the colonic epithelium is another important factor(Fig. 2D): First, water is absorbed by the colonic epithelium, whichleads to a gradient of flow rates along the colon and has a con-centrating effect on luminal content. Second, transporters in theepithelium import SCFAs, thereby shifting pH to more neutralvalues; this uptake is further coupled to the secretion of bicarbonate,which, together with other luminal components, acts as a buffer tostabilize pH. On the other hand, uptake of SCFAs by cross-feedingbacteria is not expected to play a significant role (SI Appendix,section 2.8). We derived quantitative estimates for all these factorsas explained briefly in Fig. 2 and elaborated in detail in SI Appendix.We then integrated the key processes described in Figs. 1 and

2 to formulate a comprehensive mathematical model for the coarse-grained bacterial growth dynamics in the human colon. The dy-namics are described by a set of differential equations, explicitlymodeling the spatiotemporal evolution of the densities of Bacter-oidetes and Firmicutes, as well as of the concentrations of nutrients,bicarbonate, and SCFAs. The structure of the model is outlined inMaterials and Methods and described in detail in SI Appendix, sec-tion 5. Importantly, all parameters used in the model (summarizedin SI Appendix, Tables S1 and S2) are either derived directly fromexperimental data on bacterial physiology or deduced from ananalysis of published data without resorting to fitting parameters.

Growth Dynamics for Standard Western Diet. The main nutrientsources of bacteria in the colon are complex dietary carbohydratesthat cannot be absorbed by the small intestine. For a healthy adultand a typical Western diet, an estimated 50–60 g of such ferment-able carbon reaches the colon every day (23–25). Roughly 20 g ofthis fermentable carbon is nonstarch fiber (26, 27), of which about75% are metabolized in the colon (28); the remaining 30–40 greaching the colon consist of resistant starch and unabsorbed sugars,for which utilization by bacteria is even higher (29). This corre-sponds to roughly 300 mmol/d glucose equivalents, or 200 kcal/d (SIAppendix, section 2.6). Here, we focus on the primary consumptionof these carbohydrates, and thus the main turnover of bacterialbiomass in the colon. If we simulate bacterial growth dynamicsunder this nutrient inflow for 5 d, we observe stable bacterialdensities (Fig. 3A); see SI Appendix, Fig. S3, for the full temporalevolution starting from a low-density initial state. Bacteroidetes dobetter at the start of the proximal colon (Fig. 3B, gray region),where nutrients are plentiful (Fig. 3C, orange line) and pH is neutral(Fig. 3D). Due to fast bacterial growth, nutrients are consumed andSCFA secretion dominates over epithelial SCFA uptake in the as-cending colon (Fig. 3C, light blue region), leading to increasingSCFA concentrations, a fast drop in pH, and a growth advantage forFirmicutes (Fig. 3 A and B, blue lines). Further into the colon (Fig.3C, pink region), SCFA uptake dominates over SCFA production(black line) and bicarbonate secreted by epithelial cells accumulates(Fig. 2, Bottom), leading to a rise in pH back to neutral values (Fig.3D). Strong bacterial growth is not possible in the distal colon (i.e.,the transverse and descending colon and the rectum; Fig. 2A), as allmajor nutrient sources have been depleted earlier (Fig. 3 B and C).The results presented in Fig. 3 reproduce a number of published

observations remarkably well: The absolute magnitude of bacterialdensities in the beginning of the colon (16) and in feces (1, 19), thesharp drop in pH at the beginning of the colon and the later rise toneutral values (24, 30), as well as SCFA concentrations in the dif-ferent parts of the colon (24, 30) have all been measured in humansubjects and are quantitatively captured by our model without pa-rameter fitting; see SI Appendix, Table S3, for a comparison ofmodeling results with literature data.These results show that bacterial growth, at least of the primary

carbohydrate consumers, takes place in the proximal colon (Fig. 3B)

A B

C D

Fig. 1. Characterizing the growth physiology of Bacteroidetes and Firmicutes.Measurements for axenic cultures of Bt and Er as representatives of their re-spective phyla. (A) Excretion of the main fermentation products (SCFAs), (B) thebiomass [optical density (OD) reached per millimolar glucose] and total SCFAs(millimolar SCFA secreted per unit OD) yields. (C) pH dependences of the growthrate for both strains. Circles indicate measured values, and lines represent logisticfits to the data. (D) Illustration of the differential pH feedback effect: BothBacteroidetes and Firmicutes produce SCFAs that contribute to the acidificationof their local environment. This acidification in turn inhibits bacterial growth,more strongly for Bacteroidetes than for Firmicutes. Because Bacteroidetesgrows faster than Firmicutes at neutral pH (C), it has a growth advantage overFirmicutes at higher pH, whereas the reverse is true at lower pH. The valuesshown in A and B were averaged over different pH values characterized; see SIAppendix, Fig. S1, for the full dataset of SCFA excretion at various pH values.Error bars denote SD.

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where nutrients arriving from the small intestine are plentiful (Fig.3C). As a result of this localized growth, the microbiota compositiondoes not change much downstream of the proximal colon. Thesefindings clearly illustrate the importance of understanding spatialbacterial growth dynamics in the colon: Fecal microbiota compo-sition is a consequence of bacterial growth in the proximal colon.To predict how changes in bacterial and host physiology may

affect microbiota composition, we performed a sensitivity analysisfor a number of physiologically relevant parameters (see SI Ap-pendix, Table S4, for a comprehensive list of parameters). Changesin microbiota composition resulting from a variation in the strengthof peristaltic mixing, in the buffer capacity of the colonic lumen, andthe SCFA uptake rate of the colonic epithelium are shown in SIAppendix, Fig. S4. In the following, we discuss nutrient availabilityand water uptake by the colonic epithelium, which we found toexert large impacts on microbiota composition.

The Effect of Nutrient Inflow.Diet has been shown to have a strongand immediate impact on the composition of the gut microbiota(31–33), and a link between obesity, nutrition, and the gutmicrobiota has been proposed (7, 8, 32, 34, 35). Both qualitativeand quantitative changes in diet can lead to different amounts ofunabsorbed nutrients flowing into the colon (29). We thereforestudied the effect of nutrient inflow on bacterial growth.Changing the rate of nutrient inflow strikingly changes phyla

composition (Fig. 4A). This is a direct consequence of the differ-ential pH feedback depicted in Fig. 1D: At low nutrient inflow rates,only low amounts of SCFAs can be produced by fermentativegrowth, resulting in only a moderate drop in luminal pH (Fig. 4B,black lines). This allows Bacteroidetes to grow faster than Firmi-cutes, thus leading to a higher relative abundance of Bacteroidetes(Fig. 4A, Left). At higher nutrient inflow rates, more fermentationtakes place, and the elevated SCFA secretion leads to a strongerdrop in pH (Fig. 4B, orange lines). This leads to a growth advantageof Firmicutes (Fig. 4A, Right). Thus, with increasing nutrient levels,the competitive advantage shifts from Bacteroidetes to Firmicutesdue to their differential pH response.Concomitantly with a change in phyla composition, the compo-

sition of secreted fermentation products (SCFAs) changes (Fig. 4C).The total rate of SCFA uptake by the epithelium represents theenergy the host can derive from the nutrients reaching the colon. Atlow nutrient inflow rates, where Bacteroidetes dominate (Fig. 4A),most host calories are derived from acetate and succinate (Fig. 4 Cand D), mainly secreted by Bacteroidetes (Fig. 1A). In contrast, athigh nutrient inflow where Firmicutes dominate, acetate, butyrate,and lactate (mainly secreted by Firmicutes; Fig. 1A) are dominant(Fig. 4C). This can have important consequences for the host be-cause different SCFAs are used differently (36) and exert differentphysiological effects; especially butyrate has been suggested to havesignificant health benefits, ranging from antiinflammatory effects(37, 38) to the promotion of apoptosis in tumor cells (39).

The Effect of Colonic Water Absorption. The rate of epithelial wateruptake is another important factor setting colonic microbiotacomposition. If water uptake is high, Firmicutes dominate (Fig.5A). This effect of water uptake can be rationalized by consid-ering the concentration of luminal contents: by removing water,SCFA concentrations increase. This, in turn, leads to strongeracidification of the environment (Fig. 5B, orange curve) and agrowth advantage for the Firmicutes (Fig. 1 C and D), leading toa higher relative abundance of this phylum. Conversely, weakerwater absorption leads to lower SCFA concentrations, and thepH remains nearly neutral (Fig. 5B, black curve). This allowsBacteroidetes to outcompete Firmicutes (Fig. 1 C and D), resultingin their higher relative abundance at low water uptake (Fig. 5A).

inflow1.5 l/day

outflow0.1 l/day

water absorption

position [cm]

velo

city

[μm

/s]

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epithelium

SCFAbicarbonate

aerobic energygeneration

buffer

bacteriabacteria

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[H+]

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cecumascending colontransverse colondescending colonsigmoid colonrectum

Length colon: 1.9m

Diameter luminal tube: 2.4 cm

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10

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50 100 1500

Effective diffusion: D=106 μm2/s

active mixing by wall contractions

}

}

proximalcolon

distalcolon

B

A

C

D

Fig. 2. Physiological parameters of the human colon. (A) Anatomical di-mensions. Based on measurements of human colonic anatomy during autopsy(49, 50), X-ray and CT imaging using contrast media (51, 52), and magneticresonance tomography imaging (53), we derived operational numbers for thelengths, surface areas, and luminal diameters of the different colonic segments(SI Appendix, section 2.1). (B) Luminal flow. About 1.5 L of fluid reaches theproximal colon every day (54, 55). The epithelium absorbs most of this volume(54, 56, 57), and only 100–200 mL per day exit the colon as feces (57). Thiscontinuous water uptake along the colon leads to a steep gradient in luminalflow rates. We calculated an average flow velocity of about 30 μm/s at thebeginning of the colon that drops to about 5 μm/s by the end of the ascendingcolon (see SI Appendix, section 2.2, for details). (C) Mixing of luminal contents.Contractions of the intestinal walls can generate local mixing (11, 22, 58).Based on data on the mixing of radiolabeled dyes in the large intestine (40),we derive that the measured distributions can be approximated by an ef-fective diffusion constant of D ∼ 106 μm2/s, a value orders of magnitudehigher than molecular diffusion (see SI Appendix, Fig. S9 and section 2.4,for full analysis). (D) Epithelial SCFA uptake, bicarbonate excretion, andbuffer chemistry. Bacterial fermentation leads to production of SCFAs,which are taken up by the gut epithelium and contribute to the host’senergy intake. SCFA uptake is coupled to the excretion of bicarbonate,

which, in equilibrium with CO2 and other luminal components, buffer theluminal acidity (pH = −log[H+]). All calculations are based on the measuredcharacteristics of epithelial transporters and buffer capacity of the lumen(59); see SI Appendix, sections 2.8, 2.9, and 4, for details.

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Importantly, such a change in colonic water uptake can be inducedtherapeutically in human patients using commonly used drugs (e.g.,Senna, Loperamide).Water uptake by the epithelium is coupled to colonic transit time:

If less water is taken up, luminal contents move faster (40) (Fig. 5Cand SI Appendix, Fig. S5). Accordingly, transit time itself is correlatedwith the consistency of feces (41, 42) which can be quantified by theBristol stool scale (BSS), a diagnostic measure to formally score fecalconsistency on a scale from 1 (separate hard lumps) through 7 (wa-tery without solids; see SI Appendix, section 5.8, for a detailed analysisof the relation between transit time and BSS) (41). In agreement withour predictions (Fig. 5), recent epidemiological studies have shownthat BSS is the major explanatory variable for microbiota compositionin healthy humans (43, 44): Higher BSS scores (less colonic wateruptake) correspond to a higher relative abundance of Bacteroidetes.

DiscussionIn this study, we formulated a quantitative model that integratesextensive literature data on human physiology (Fig. 2) and mea-sured bacterial growth characteristics (Fig. 1 and SI Appendix, Fig.S1). Bacteria grow in the colon and excrete acidic fermentationproducts, which in turn differentially affect growth of the domi-nant phyla. Human physiology plays an important role in de-termining the relative abundances of these phyla by affecting pHbalance, which drives this feedback. All components of this dy-namics are summarized in SI Appendix, Fig. S6. Our model re-produces important and well-quantified physiological observableswithout ad hoc fitting (SI Appendix, Table S3, and Fig. 3). Westudied in detail how nutrient inflow (Fig. 4) into the colon andwater uptake (Fig. 5) affect microbiota composition.Sequencing analysis of fecal samples has shown great variation

between healthy individuals: The Human Microbiome Projectfound, for example, that the relative abundance of Bacteroidetesand Firmicutes varied strongly between 242 analyzed samples ofhealthy individuals (Fig. 6, Inset). Our analysis shows that smallvariations in nutrient inflow and colonic water uptake, which de-termines stool consistency, can lead to a large shift in relative phylaabundances (Fig. 6): For the observed distribution of these param-eters in humans (Fig. 6, highlighted area; SI Appendix, sections2.6 and 5.8), microbiota composition can change from mostlyBacteroidetes to mostly Firmicutes. These compositions are com-parable to observations from the HumanMicrobiome Project (Fig. 6,Inset). Furthermore, microbiome sequencing has confirmed nutrientinflow, transit time, and water content to be crucial determinants of

microbiota composition (31, 32, 45, 46), with stool consistency (BSS)identified as the single most important factor explaining microbiotavariation in a large-scale epidemiological study (44). Our results offera minimal explanation for these variations: Nutrient inflow and stoolconsistency affect microbiota composition via changes in luminal pH.For more nutrient inflow, more fermentation products are produced.For drier stool consistency, more colonic water uptake leads tohigher concentrations of fermentation products. Both of these effectslead to a drop in pH and thus, via the differential pH feedback onbacterial growth, to an advantage for Firmicutes.We have shown that detailed and quantitative data on human

and bacterial physiology can be used to understand their interac-tions, leading to mechanistic insights into main factors shaping thecomposition of microbiota in the gut. Our approach offers thepossibility to understand mechanistically how new interventionstrategies influencing different aspects of human physiology couldaffect microbiota composition. This iterated dialogue can lead notonly to conceptual advances in the understanding of the functioningof the gut microbial community but also to possible new angles fortherapeutic approaches for the array of health issues that have beenconnected to the gut microbiota, ranging from inflammatory boweldiseases to infection and cancer (47).

A

B

C

D

Fig. 3. Spatial profiles along the colon predicted for standard Western diet.Results of the model with a nutrient influx of 300 mmol glucose equivalents perday entering the colon. Spatial profiles for different variables are plotted:(A) local densities and (B) growth rates of Bacteroidetes (red) and Firmicutes(blue); (C) local nutrient (orange) and total SCFA (black) concentrations; (D) localpH values. The background colors correspond to the different sections of thecolon as illustrated in Fig. 2A. Only the first 100 cm of the colon are shown here, asall observables remain effectively unchanged further downstream. Parameters aregiven in SI Appendix, Tables S1 and S2. Results shown here are for simulationsafter 120 h. Temporal dynamics along the length of the colon is shown in SIAppendix, Fig. S3, for recovery from a low initial bacterial density profile.

A

C

B

Fig. 4. Changing nutrient intake affects microbiota composition and SCFAavailability. The spatiotemporal dynamics of bacterial growth was analyzed fordifferent rates of nutrient influx (Nin, in millimoles of glucose equivalents per day).(A) Relative abundance of Bacteroidetes and Firmicutes in the distal colon (mim-icking “fecal” content), depending on nutrient influx. (B) pH profiles along thelength of the colon; each colored line represents the result of a specific nutrientinflux. (C) Epithelial uptake of different SCFAs (integrated along the length of thecolon) for different nutrient influx. SCFA ratios are calculated based on measuredexcretion rates (Fig. 1A) and model results for phyla composition in A. Table pro-vides the relationship between the nutrient influx (Nin), their corresponding energycontent (Ein), and the amount of energy taken up by the epithelium in the form ofSCFAs (Eup). The case of Nin = 300 mmol/d corresponds to the results shown in Fig.3. Other parameters are as in SI Appendix, Tables S1 and S2. Values in A for po-sition x = 1.89m (end of colon). Values in C estimated by average excretion profilesof different strains (Fig. 1A and SI Appendix, section 5.7). Simulation for 120 h.Profiles of other variables are shown in SI Appendix, Fig. S7 A–C.

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Materials and MethodsBacterial Strains and Culture Conditions. Bt (ATCC 29148) and Er (ATCC 33656)were grown in media at various pH values, and their growth rates weremeasured by monitoring optical densities at regular time intervals. See SIAppendix, section 1.1, for detailed experimental methods.

Metabolite Analysis. Samples were taken at four time points during exponentialgrowth, andmetabolite concentrationsweremeasured usingHPLC equippedwitha refractive index detector (see SI Appendix for details). Metabolite concentrationswere quantified by comparing the areas under the respective peaks with a baselineof known metabolite concentrations. See SI Appendix, section 1.2, for details.

Modeling Bacterial Growth Dynamics in the Human Colon. We model thespatiotemporal dynamics in the colon by a set of partial differential equa-tions, explicitly considering the density of Bacteroidetes ρBðx, tÞ, the densityof Firmicutes ρFðx, tÞ, and the concentrations of nutrients nðx, tÞ, total SCFAssðx, tÞ, and total carbonate cðx, tÞ. x and t denote position along the colonand time. pH values, pHðx, tÞ follow from total SCFAs and total carbonate(see below). Bacterial densities are described by the following equations (SIAppendix, Eqs. 8 and 9):

∂ρB∂t

=D∂2ρB∂x2

−∂∂x

½vðxÞρB�+ λBðn,pHðx, tÞÞ · ρB,

∂ρF∂t

=D∂2ρF∂x2

−∂∂x

½vðxÞρF �+ λF ðn,pHðx, tÞÞ · ρF .[1]

Active mixing by wall contractions is described by an effective diffusionconstant D (Fig. 2 and SI Appendix, Figs. S1 and S4, and section 2.4). Netluminal flow is described by a convection term vðxÞ, with a position-dependent flow rate reflecting active water uptake in the proximal colon(Fig. 2 and SI Appendix, section 2.2).

Growth dynamics is governed by the growth rates, λB and λF, which de-pend on the local nutrient concentration n through the Monod form (SIAppendix, Eq. 9):

λBðn,pHÞ= λmax,BðpHÞ · nn+KM,B

and λFðn,pHÞ= λmax,FðpHÞ · nn+KM,F

, [2]

with KM,B and KM,F being the Monod constants. λmax,B and λmax,F are the max-imal growth rates at saturated nutrient concentrations; they depend on the

local pH, pHðx, tÞ, according to the form quantified by our experiments(Fig. 1 and SI Appendix, Fig. S1 and section 3.1). Monod constants havebeen estimated from measurements with Escherichia coli strains (SI Ap-pendix, Table S2) (48). The exact values of these Monod constants playonly a minor role for the dynamics.

Nutrient consumption is described by the following equation (SI Appendix,Eq. 10):

∂n∂t

=D∂2n∂x2

−∂∂x

½vðxÞnðx, tÞ�− λBðn,pHÞρB�YB − λF ðn,pHÞρF

�YF , [3]

with the constant yield factors YB and YF as measured (Fig. 1 and SI Ap-pendix, Fig. S1 and section 5.3). Note that the same effective diffusionconstant D is used for the small nutrient molecules and the much largerbacterial cells, because in contrast to molecular diffusion, mixing dynamics issimilar for both (11). A similar equation is used to describe the total con-centration of excreted short chain fatty acids, s, as follows:

∂s∂t

=D∂2s∂x2

−∂∂x

½vðxÞs�+ eB,SCFAλBðn,pHÞρB + eF,SCFAλFðn,pHÞρF − JSCFAðsÞ [4]

(SI Appendix, Eq. 13) with eB,SCFA and eF,SCFA describing the measured ex-cretion rates of total SCFAs (Fig. 1 and SI Appendix, Fig. S1). Additionally,active uptake of SCFAs is described by a concentration-dependent rateJSCFAðsÞ (Fig. 2 and SI Appendix, section 5.5) as observed in humansand mice.

The dynamics of the carbonates (CO2, carbonic acid, and bicarbonate), oftotal concentration cðx, tÞ, is composed of several similar effects. The first isthe production of CO2 from bacterial metabolism, with excreted CO2 beingin dissociation equilibrium with carbonic acid and bicarbonate in a pH-dependent manner. Dynamics is captured by the following equation (SIAppendix, Eq. 14):

A

C

B

Fig. 5. The effect of colonic water uptake on microbiota composition.(A) Relative abundances of Bacteroidetes and Firmicutes in the distal colon fordifferent values of water uptake. (B) pH profiles along the length of the colon;each colored line represents the result for a specific level of water absorption(water-absorpt). (C) Table relates water uptake to colonic transit times (TT) andstool consistency (BSS); see SI Appendix, section 5.8 and Fig. S5, for how theserelations were determined. Water uptake of 0.25 mL/h·cm2 corresponds tothe results shown in Fig. 3. Other parameters are as in SI Appendix, TablesS1 and S2. Values in A for position x = 1.89 m (end of colon). Simulations for120 h. Profiles of other variables are shown in SI Appendix, Fig. S7 D–F.Similar results are observed for changes in water inflow and outflow rates (SIAppendix, Fig. S8).

Fig. 6. Variation in microbiota composition for typical physiological parametersof the human host. Summarized results of our model investigating how the in-terplay of human and bacterial physiology mediated by water flow, absorption,and active mixing shape microbiota composition. The 3D plot shows the fractionof Firmicutes depending on the nutrient influx rate and the rate of water uptake,as manifested by stool consistency (BSS). The bright area highlighted on the 2Dprojection indicates the parameter variations estimated for healthy adults con-suming aWestern diet (SI Appendix, sections 2.6 and 5.8). The bar plot in the Insetshows data on phyla composition in 242 healthy subjects from the HumanMicrobiome Project (6) (heat map corresponds to heat map in main panel). Theobserved variation in phyla can be readily accounted for by differences in nutrientintake and stool consistency. Corroborating this observation, BSS has been iden-tified as the single most important determinant for microbiota compositionamong 69 covariates studied (44). Parameters are as in SI Appendix, Tables S1 andS2. Simulation for 120 h. Values for x = 1.89 m (end of colon).

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∂c∂t

=D∂2c∂x2

−∂∂x

½vðxÞc�+ eB,CO2λBðn,pHÞρB + eF,CO2λFðn,pHÞρF+ αc · JSCFAðsÞ− ecðc,pHÞ,

[5]

with eB,CO2 and eF,CO2 denoting the estimated rate of CO2 production (SI Appendix,Table S2 and section 3.2). The second effect involves the epithelial excretion ofbicarbonate, which is driven by a 1:1 exchangewith the uptake of SCFAs for a highfraction αC of SCFA transporters (Fig. 2 and SI Appendix, section 2.8). A third effectis that, as confirmed by measurements, CO2 can diffuse through the epithelialmembrane in a pH-dependent manner. This effect is modeled by the termecðc,pHÞ, which includes the observed membrane permeability and the pH-dependent dissociation of CO2 into bicarbonate and protons.

Finally, local pH is obtained from the local SCFA and carbonate concen-trations, pHðx, tÞ=W ½s, c� (SI Appendix, Eq. 6) in a way that depends on thebuffer properties of the lumen (SI Appendix, section 4). In short, pH followsobserved buffer behavior of the luminal fluid and a self-consistent solutionof the dissociation dynamics: For lower pH, the buffer components in the

lumen have to buffer more protons coming from SCFAs and total carbonate(full discussion in SI Appendix, section 4).

Details of model implementation, including boundary conditions andnumerical solution, are given in SI Appendix, section 5. See Dataset S1 for thesource code of the simulations. All of the model parameters used are sum-marized in SI Appendix, Tables S1 and S2.

ACKNOWLEDGMENTS. We thank John Cummings and the late GeorgeMacfarlane for initial insights into the field of colon physiology and thegut microbiota. We further thank Alfonso Die for help in setting up HPLCmeasurements, and Christophe Chassard, Alex Groisman, Shasha Jumbe,Anna Melbinger, and Igor Segota for useful discussions. This work is sup-ported by Grant OPP1113361 from the Bill and Melinda Gates Foundation.T.H. acknowledges additional support by NIH Grant R01GM109069. J.C. ac-knowledges support by German Academy of Sciences Leopoldina (LPDS2011-10). M.A. is supported by a fellowship from the Swiss National ScienceFoundation (P300PA 160965) and is a nonstipendiary European MolecularBiology Organization Fellow (ALTF 344-2015).

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